What's the origin of 'Butter her up?'

We never use this term in relation to men, do we?

Yes, we do:

A: Who’s your professor this semester?
B: Professor Ornstein.
A: Oh, he’s really tough. If you want to get a good mark, you’d better start buttering him up!
B: How should I do that?
A: Start by telling him that he is the best professor you’ve ever had. Then keep going….

http://www.idiomeanings.com/butter-up/

My coworker, hoping for a raise, is always buttering up the boss.
If we butter up the bartender, maybe he'll buy us a drink.

from The American Heritage® Dictionary of Phrasal Verbs

If you butter up Dad, he'll let you borrow the car.

This last one, quoted from The American Heritage® Dictionary of Idioms, not only puts an end to your theory, it also adds an explanation:

This term transfers the oily, unctuous quality of butter to lavish praise. [c. 1700]

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cf. grease the wheels

This may perhaps better explain the term "Butter her up" more precisely. The quote is taken from Variety 10th Dec.2016.

The director addressed the non-consensual rape scene in a recently resurfaced interview from 2013. “Last Tango in Paris” director Bernardo Bertolucci confessed that he and Marlon Brando conspired against actress Maria Schneider during a rape scene in which the actor used a stick of butter as lubricant to simulate sex.

I don't think the origin of ‘butter someone up’ is plainly related to ‘sex’. According to TheIdioms, butter someone up has been derived directly from ‘the act of buttering (spreading butter on) a toast of bread to make it softer and tastier so that the person eating it gets more satisfaction from it’. That site further says that this phrase ‘came to represent spreading nice things about someone [flattering] just so you could get something in return’.

Dictionary.com says that butter up ‘transfers the oily, unctuous quality of butter to lavish praise’.

Phrases.com also agrees with the above explanation:

When we butter up the slice of bread, we actually make it more delicious. Similarly, when we need a favor and support of someone, we often praise or flatter him/her

Grammarly associates its origin with an ancient religious act in India, it says that ‘The devout would throw butter balls at the statues of their gods to seek favor and forgiveness’, though it doesn't sound plausible to me.